A copy of the diagram is shown below
Point D is the intersection of three angle bisector.
BE is the angle bisector of ∠B
CF is the angle bisector of ∠C
AG is the angle bisector of ∠A
Point D is also the intersection between three perpendicular bisector
BE is the perpendicular bisector of AC
AG is the perpendicular bisector of BC
CF is the perpendicular bisector of AB
Hence the correct statements is statement 1 and statement 4